Home
Class 12
MATHS
If C(r ) = (n!)/(r!(n - r)!), then prove...

If `C_(r ) = (n!)/(r!(n - r)!)`, then prove that
`sqrt(C_(1)) + sqrt(C_(2)) + …. + sqrt(C_(n)) sqrt(n(2^(n) - 1))`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    MOTION|Exercise Exercise -4 (Level - I) ( Previous Year )|12 Videos

  • BINOMIAL THEOREM

    MOTION|Exercise Exercise -4 (Level - II) ( Previous Year )|7 Videos

  • BINOMIAL THEOREM

    MOTION|Exercise Exercise - 2 (Level - II) (Multiple Correct ) (MIXED PROBLEMS )|3 Videos

  • BASIC MATHEMATIC & LOGARITHM

    MOTION|Exercise Exercise - 4|4 Videos

  • CIRCLE

    MOTION|Exercise Exercise - 4 | Level - II (Previous Year | JEE Advanced|22 Videos

Similar Questions

Explore conceptually related problems

If C_r=(n !)/([r !(n-r)]), the prove that sqrt(C_1)+sqrt(C_2)+.......sqrt(C_n) lt sqrt(n(2^n-1)) ="">

If (1+x)^(n)=sum_(r=0)^(n)C_(r)x^(r), then prove that C_(1)+2c_(2)+3C_(1)+...+nC_(n)=n2^(n-1)...

If (1+x)^(n)=sum_(r=0)^(n)C_(r)x^(r) then prove that C_(0)+(C_(1))/(2)+......+(C_(n))/(n+1)=2

If (1+x)^(n)=sum_(r=0)^(n)C_(r)x^(r) then prove that C_(1)+2C_(2)+3C_(3)+....+nC_(n)=n2^(n-1)

Prove that sum_(r=0)^(n)r(n-r)C_(r)^(2)=n^(2)(^(2n-2)C_(n))

If n>2, then prove that C_(1)(a-1)-C_(2)xx(a-2)+...+(-1)^(n-1)C_(n)(a-n)=a, where C_(r)=^(n)C_(r)

lim_ (n rarr oo) sum_ (n = 1) ^ (n) (sqrt (n)) / (sqrt (r) (3sqrt (r) + 4sqrt (n)) ^ (2))

Prove that .^(n)C_(r)+^(n)C_(r-1)=^(n+1)C_(r)

MOTION-BINOMIAL THEOREM -Exercise -3 ( Subjective )
  1. If (1 + x)^(n) = C(0) = C(1) x + C(2) x^(2) + …+ C(n) x^(n) , find...

    Text Solution

    |

  2. Prove that sqrt(C1) +sqrt(C2) +sqrt(C3)+...+sqrt(Cn)le 2^(n-1) +(n-1)/...

    Text Solution

    |

  3. If C(r ) = (n!)/(r!(n - r)!), then prove that sqrt(C(1)) + sqrt(C(2)...

    Text Solution

    |

  4. Sum of all the digits of the coefficient of x^(5) in the expansion of ...

    Text Solution

    |

  5. Find the coefficient of x^(4) in the expansion of (1+x+x^(2)+x^(3))^(1...

    Text Solution

    |

  6. Find the coefficients of x^(4) in the expansions of (2 - x + 3x^(2...

    Text Solution

    |

  7. Let a = (72!)/(36!)^2-1 , then (A) a is odd (B) a is divisible by 7...

    Text Solution

    |

  8. find the sum of the series sum(r=0)^n(-1)^r *"^nCr[1/(2^r)+(3^r)/(2^(...

    Text Solution

    |

  9. Given that (1+x+x^2)^n=a0+a1x+a2x^2+........+a(2n)x^(2n) find the val...

    Text Solution

    |

  10. Given that (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+......+a(2n)x^(2n), f...

    Text Solution

    |

  11. Given that (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+......+a(2n)x^(2n), f...

    Text Solution

    |

  12. If n(j(r))=((1-xn)(1-x(n-1))(1-x^(n-2)).......(1-x^(n-r+1)))/((1-x)(1-...

    Text Solution

    |

  13. Prove that sum(k=0)^n ^nCk sinKx.cos(n-K)x=2^(n-1)sin nx

    Text Solution

    |

  14. The expressions 1+x,1+x+x^2,1+x+x^2+x^3.............1+x+x^2+.............

    Text Solution

    |

  15. Find the coefficients of x^(6) in the expansion of (ax^(2) + bx +...

    Text Solution

    |

  16. Find the coefficient of x^2 y^3 z^4 in the expansion of (ax-by+cz)^9

    Text Solution

    |

  17. Find the coefficient of x^2 y^3 z^4 in the expansion of (ax -by +cx...

    Text Solution

    |

  18. If sum(r=0)^(2n)ar(x-2)^r=sum(r=0)^(2n)br(x-3)^ra n dak=1 for all kgeq...

    Text Solution

    |

  19. Show that the integral part in each of the following is odd. n in N. ...

    Text Solution

    |

  20. Show that the integral part in each of the following is even. n in N....

    Text Solution

    |